1 PARAMETRIC VERSUS NONPARAMETRIC STATISTICS Heibatollah Baghi, and Mastee Badii.
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Transcript of 1 PARAMETRIC VERSUS NONPARAMETRIC STATISTICS Heibatollah Baghi, and Mastee Badii.
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PARAMETRIC VERSUS PARAMETRIC VERSUS NONPARAMETRIC STATISTICSNONPARAMETRIC STATISTICS
Heibatollah Baghi, and Heibatollah Baghi, and
Mastee BadiiMastee Badii
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Parametric AssumptionsParametric Assumptions
Parametric Statistics involve hypothesis Parametric Statistics involve hypothesis about population parameters (e.g., about population parameters (e.g., µ, µ, ρρ).).
They require assumptions about the They require assumptions about the population distribution. For example, the population distribution. For example, the assumptions for t test for independent assumptions for t test for independent samples are:samples are:a)a) Each of the two populations of observations is Each of the two populations of observations is
normally distributed normally distributed b)b) The populations of observations are equally The populations of observations are equally
variable : that is variable : that is σσ22 = = σσ2.2. (Assumption of (Assumption of homogeneity of variance ) homogeneity of variance )
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Nonparametric AlternativeNonparametric Alternative
The parametric assumptions cannot The parametric assumptions cannot be justified: normal distribution, be justified: normal distribution, equal variances, etc.equal variances, etc.
The data as gathered are measured The data as gathered are measured on nominal or ordinal dataon nominal or ordinal data
Sample size is small.Sample size is small.
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Spearman Rank CorrelationSpearman Rank Correlation
The Spearman rank correlation is The Spearman rank correlation is used when:used when: Distribution assumptions required by Distribution assumptions required by
Pearson r are in question Pearson r are in question Small sample sizeSmall sample size
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ExampleExample
X: The student’s popularity X: The student’s popularity measuremeasure
Y: The student’s average academic Y: The student’s average academic achievement achievement
Research questionsResearch questions : Is : Is popularity related to popularity related to achievement ?achievement ?
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Test of Association Using Test of Association Using Spearman Rank CorrelationSpearman Rank Correlation
Because of doubts regarding the Because of doubts regarding the distributional assumptions coupled with distributional assumptions coupled with small sample size, select the Spearman small sample size, select the Spearman Rank Correlation to answer this questionRank Correlation to answer this question
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
Spearman rankcorrelation
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
Differencebetween ranks
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
Num
ber o
f case
s
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
X: The student’s popularity measureY: The student’s average academic
achievement
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
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Calculation of Spearman Rank Calculation of Spearman Rank CorrelationCorrelation
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Calculation of Spearman Calculation of Spearman Rank CorrelationRank Correlation
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Calculation of Spearman Calculation of Spearman Rank CorrelationRank Correlation
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Test of SignificanceTest of Significance
Calculated rCalculated rRankRank= -0.26= -0.26 Critical value for alpha 0.05 for Critical value for alpha 0.05 for
Spearman Rank Correlation with 8 Spearman Rank Correlation with 8 subjects = 0.738subjects = 0.738
Calculated rCalculated rRanksRanks is less than critical value is less than critical value The relation between Popularity and The relation between Popularity and
academic achievement is not academic achievement is not statistically significantstatistically significant
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When to Use Which TestWhen to Use Which Test
Nominal Data
Two-group case Chi-square t test
K – group case Chi-square ANOVA
Dependent groupsMcNamer test
Association Chi-square Pearson r
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When to Use Which TestWhen to Use Which Test
Nominal Data
Ordinal Data
Two-group case Chi-squareMann-Whitney U t test
K – group case Chi-squareKruskal-Wallis H ANOVA
Dependent groupsMcNamer test
Sign Test or Wilcoxon
Association Chi-squareSpearman rank Pearson r
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When to Use Which TestWhen to Use Which Test
Nominal Data
Ordinal Data
Interval or Ratio data
Two-group case Chi-squareMann-Whitney U t test
K – group case Chi-squareKruskal-Wallis H ANOVA
Dependent groupsMcNamer test
Sign Test or Wilcoxon
Paired t test
Association Chi-squareSpearman rank Pearson r
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Take Home LessonTake Home Lesson
Spearman Rank Correlation Spearman Rank Correlation can be used on ordinal datacan be used on ordinal data